# A shaped stepladder physics problem?

1. Dec 3, 2012

### physicsmajor9

1. The problem statement: A stepladder consists of two halves, hinged at the top, and connected by a tie rod that keeps the two halves from spreading apart. In this particular instance, the two halves are 2.50 m long, the tie rod is connected to the center of each half and is 70.0 cm long. An 800-N person stands 3/5 of the way up the stepladder, as shown in the figure. Neglecting the weight of the ladder, and assuming that the ladder is resting on a smooth floor, what is the tension in the tie rod?
Picture http://session.masteringphysics.com/problemAsset/1396325/2/p8.70.jpg

2. Relevant equations
ƩFx=0
ƩFy=0
Ʃtorque=0

3. The attempt at a solution:
I know I should look at the ladder as if it were in 2 seperate pieces but I have no idea how to start or what to look at.
I also tried drawing free body diagrams for each but it confuses me even more

2. Dec 3, 2012

### PhanthomJay

It is usually best to solve for the external reaction forces (at the base) first. Since the floor is frictionless, the forces at each support must be in a vertical direction only. You can solve for them by summing torques about one end = 0 and using Newton 1. This can be done without having to take the ladder apart in FBD's. Once you solve for them, then now draw a FBD of one side of the ladder, and sum torques about the top to solve for the horizontal force in the tie rod (the force in the tie rod must be horizontal only, since it is a 2-force member that canot support vertical loads).